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Label Dim. \(A\) Field CM RM Traces Fricke sign $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
152.1.g.a \(1\) \(0.076\) \(\Q\) \(\Q(\sqrt{-38}) \) None \(-1\) \(1\) \(0\) \(-1\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
152.1.g.b \(1\) \(0.076\) \(\Q\) \(\Q(\sqrt{-38}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+q^{2}-q^{3}+q^{4}-q^{6}-q^{7}+q^{8}+\cdots\)
152.1.k.a \(2\) \(0.076\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots\)
152.1.u.a \(6\) \(0.076\) \(\Q(\zeta_{18})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-3\) \(0\) \(0\) \(q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots\)
152.2.a.a \(1\) \(1.214\) \(\Q\) None None \(0\) \(-2\) \(-1\) \(-3\) \(+\) \(q-2q^{3}-q^{5}-3q^{7}+q^{9}-3q^{11}+\cdots\)
152.2.a.b \(1\) \(1.214\) \(\Q\) None None \(0\) \(1\) \(0\) \(3\) \(-\) \(q+q^{3}+3q^{7}-2q^{9}+2q^{11}+q^{13}+\cdots\)
152.2.a.c \(3\) \(1.214\) 3.3.961.1 None None \(0\) \(1\) \(1\) \(4\) \(-\) \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
152.2.b.a \(2\) \(1.214\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{2}+2\beta q^{3}-2q^{4}-4q^{6}-2\beta q^{8}+\cdots\)
152.2.b.b \(4\) \(1.214\) \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
152.2.b.c \(12\) \(1.214\) 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)
152.2.c.a \(2\) \(1.214\) \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(4\) \(q+(-1+i)q^{2}-2iq^{4}+2q^{7}+(2+2i)q^{8}+\cdots\)
152.2.c.b \(16\) \(1.214\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\beta _{6}+\cdots)q^{5}+\cdots\)
152.2.i.a \(2\) \(1.214\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(-3\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.b \(2\) \(1.214\) \(\Q(\sqrt{-3}) \) None None \(0\) \(-1\) \(4\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
152.2.i.c \(6\) \(1.214\) 6.0.2696112.1 None None \(0\) \(-1\) \(-1\) \(-4\) \(q+(-\beta _{1}+\beta _{5})q^{3}-\beta _{1}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.2.o.a \(4\) \(1.214\) \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(-6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.b \(4\) \(1.214\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
152.2.o.c \(28\) \(1.214\) None None \(-3\) \(-6\) \(0\) \(0\)
152.2.p.a \(36\) \(1.214\) None None \(-1\) \(0\) \(0\) \(-8\)
152.2.q.a \(6\) \(1.214\) \(\Q(\zeta_{18})\) None None \(0\) \(-6\) \(6\) \(3\) \(q+(-1+\zeta_{18}^{2}-\zeta_{18}^{5})q^{3}+(1-\zeta_{18}^{5})q^{5}+\cdots\)
152.2.q.b \(6\) \(1.214\) \(\Q(\zeta_{18})\) None None \(0\) \(9\) \(-6\) \(6\) \(q+(1-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}+2\zeta_{18}^{5})q^{3}+\cdots\)
152.2.q.c \(18\) \(1.214\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(-9\) \(q+(\beta _{2}-\beta _{4})q^{3}+(-\beta _{6}+\beta _{7}-\beta _{10}+\cdots)q^{5}+\cdots\)
152.2.t.a \(108\) \(1.214\) None None \(-6\) \(0\) \(0\) \(-6\)
152.2.v.a \(12\) \(1.214\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
152.2.v.b \(96\) \(1.214\) None None \(-6\) \(-6\) \(0\) \(0\)
152.3.e.a \(2\) \(4.142\) \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(14\) \(22\) \(q+\beta q^{3}+7q^{5}+11q^{7}-23q^{9}+3q^{11}+\cdots\)
152.3.e.b \(8\) \(4.142\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(-14\) \(-6\) \(q+\beta _{1}q^{3}+(-2-\beta _{4})q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
152.3.f.a \(36\) \(4.142\) None None \(2\) \(0\) \(0\) \(0\)
152.3.g.a \(3\) \(4.142\) 3.3.4104.1 \(\Q(\sqrt{-38}) \) None \(-6\) \(0\) \(0\) \(0\) \(q-2q^{2}-\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.b \(3\) \(4.142\) 3.3.4104.1 \(\Q(\sqrt{-38}) \) None \(6\) \(0\) \(0\) \(0\) \(q+2q^{2}+\beta _{1}q^{3}+4q^{4}+2\beta _{1}q^{6}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
152.3.g.c \(32\) \(4.142\) None None \(0\) \(0\) \(0\) \(-4\)
152.3.k.a \(4\) \(4.142\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(4\) \(-2\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+(-4+4\beta _{1}+\cdots)q^{4}+\cdots\)
152.3.k.b \(72\) \(4.142\) None None \(-5\) \(0\) \(0\) \(0\)
152.3.l.a \(76\) \(4.142\) None None \(-3\) \(0\) \(0\) \(-8\)
152.3.n.a \(20\) \(4.142\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(-6\) \(0\) \(-16\) \(q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
152.3.r.a \(60\) \(4.142\) None None \(0\) \(6\) \(0\) \(0\)
152.3.s.a \(228\) \(4.142\) None None \(-6\) \(0\) \(0\) \(-6\)
152.3.u.a \(12\) \(4.142\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) None \(0\) \(6\) \(0\) \(0\) \(q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
152.3.u.b \(216\) \(4.142\) None None \(-6\) \(-18\) \(0\) \(0\)
152.4.a.a \(2\) \(8.968\) \(\Q(\sqrt{57}) \) None None \(0\) \(-1\) \(-5\) \(-6\) \(-\) \(q-\beta q^{3}+(-3+\beta )q^{5}+(-5+4\beta )q^{7}+\cdots\)
152.4.a.b \(3\) \(8.968\) 3.3.3221.1 None None \(0\) \(-5\) \(2\) \(-35\) \(-\) \(q+(-2-\beta _{2})q^{3}+(1-\beta _{1}+2\beta _{2})q^{5}+\cdots\)
152.4.a.c \(3\) \(8.968\) 3.3.7057.1 None None \(0\) \(4\) \(7\) \(7\) \(+\) \(q+(1+\beta _{2})q^{3}+(2+2\beta _{1}+\beta _{2})q^{5}+(2+\cdots)q^{7}+\cdots\)
152.4.a.d \(5\) \(8.968\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(2\) \(0\) \(22\) \(+\) \(q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(4+\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
152.4.b.a \(2\) \(8.968\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2\beta q^{2}-2\beta q^{3}-8q^{4}+8q^{6}-2^{4}\beta q^{8}+\cdots\)
152.4.b.b \(56\) \(8.968\) None None \(0\) \(0\) \(0\) \(0\)
152.4.c.a \(54\) \(8.968\) None None \(2\) \(0\) \(0\) \(28\)
152.4.i.a \(14\) \(8.968\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None None \(0\) \(5\) \(5\) \(-28\) \(q+(-\beta _{1}+\beta _{7})q^{3}+(\beta _{7}+\beta _{8})q^{5}+(-2+\cdots)q^{7}+\cdots\)
152.4.i.b \(16\) \(8.968\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-5\) \(-8\) \(q-\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
152.4.o.a \(4\) \(8.968\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-30\) \(0\) \(0\) \(q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots\)
152.4.o.b \(112\) \(8.968\) None None \(-3\) \(24\) \(0\) \(0\)
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